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theorem proved term proof

rhoBandLower_lt_rhoBandUpper

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formal statement (Lean)

  43theorem rhoBandLower_lt_rhoBandUpper : rhoBandLower < rhoBandUpper := by

proof body

Term-mode proof.

  44  unfold rhoBandLower rhoBandUpper
  45  have hpos : 0 < phi⁻¹ := inv_pos.mpr phi_pos
  46  have hlt : phi⁻¹ < 1 := inv_lt_one_of_one_lt₀ one_lt_phi
  47  nlinarith
  48
  49/-- `1 - 1/φ = 1/φ²`, the golden complement relation. -/

depends on (5)

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